Infinite Insanity Cult Dogma

Some day, /prog/, I'll take you MIT. We'll go to Gerald Jay Sussman's lecture, and follow him straight to satori.

But that's not necessary just now.

For now, we are surrounded by hell. No red devils, no smell of sulfur. But hell nonetheless. A hell more grotesque than any medieval woodcut.

Instead of dramatic demons, a lifeless shuffling horde of mathematicians and physicists who believe in the cult dogma of the infinitesimal. Without souls. Without imagination. Without worth. Beyond all redemption.

Let's examine a particular case that highlights the extreme delusion that infects the minds of these zealots. I want you to watch this short propaganda video they are pushing:

https://www.youtube.com/watch?v=w-I6XTVZXww

Alternatively, you can read this:

http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/

How can the infinite series S1: 1 - 1 + 1 - 1 + ... = 1 / 2 ?!
How can the infinite series S2: 1 + 2 + 3 + 4 + ... = -1 / 12 ?!

This is what they honestly, truly believe. Their rationale for S1 is that you take the average of the two values it oscillates between. S2 can be derived by substituting in S1 through algebraic hocus pocus. How can a non-terminating recursive process that toggles a bit ever converge to something for which there is no coherent representation that follows from the natural numbers?

It should be noted that these results form the foundation of String Theory/M-Theory, which brings this whole field into question, for it is resting on a foundation of lies.

From whence does one compute a result of 1/2 from the infinite sequence of bits 01*? They are just arbitrarily assigning non-converging series rational values as a syntactic label based upon blind faith of the infinitesimal, then plugging these labels in as values for other formulae and proselytizing it as absolute truth.

It is a complete charade, a racket no different than Christianity or Judaism. It is numerology pretending to be rigorous mathematics.

I've been trying to make some Abelsense out of this, but it escapes me. How anyone can believe this and still have braincells to breathe and regulate one's cardiovascular system is beyond me!

>>5

Do those retards even know how a limit is defined? Are they abusing definitions

You see, that's the point of math definitions: they're not set in stone, and quite arbitrary. For instance, if you use the Cesaro definition of an infinite series sum, then 1 - 1 + 1 - 1 + ... does indeed equal 1 / 2.

Mathematics does not follow from experiments, is not tied to physical phenomena and is instead based on arbitrarily chosen axioms. Usually these axioms are chosen so as to be useful in describing physical phenomena, but that's not a dogma. Then again, what is useful for describing phenomena is an open question: for millenia, people thought that Euclidian geometry is The Right Thing, but then it turned out that Euclid "lied" and another set of axioms is actually closer to reality.